Explicit formulas for regularized products and series
著者
書誌事項
Explicit formulas for regularized products and series
（Lecture notes in mathematics, 1593 . Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik,
Springer-Verlag, c1994
- : gw
- : us
- タイトル別名
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Explicit formulas
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注記
Spine title: Explicit formulas
Includes bibliographical references and index
収録内容
- Explicit formulas for regularized products and series / Jay Jorgenson and Serge Lang
- A Spectral interpretation of Weil's explicit formula / Dorian Goldfeld
内容説明・目次
内容説明
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3-manifolds are given as a significant example.
目次
Explicit formulas for regularized products and series.- A spectral interpretation of Weil's explicit formula.
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